Optimal designs for indirect regression

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dc.contributor.authorBiedermann, Stefanie
dc.contributor.authorBissantz, Nicolai
dc.contributor.authorDette, Holger
dc.contributor.authorJones, Edmund
dc.date.accessioned2010-09-14T14:36:42Z
dc.date.available2010-09-14T14:36:42Z
dc.date.issued2010-09-14
dc.description.abstractIn many real life applications, it is impossible to observe the feature of interest directly. For example, scientists in Materials Science may be interested in detecting cracks inside objects, not visible from the outside. Similarly, non-invasive medical imaging techniques such as Positrone Emission Tomography rely on indirect observations to reconstruct an image of the patient's internal organs. In this paper, we investigate optimal designs for such indirect regression problems. We determine designs minimizing the integrated mean squared error of estimates of the regression function obtained by Tikhonov or spectral cut-off regularization. We use the optimal designs as benchmarks to investigate the efficiency of the uniform design commonly used in applications. Several examples are discussed to illustrate the results, in most of which the uniform design or a simple modification thereof is demonstrated to be very efficient for the estimation of the regression function. Our designs provide guidelines to scientists regarding the experimental conditions at which the indirect observations should be taken in order to obtain an accurate estimate for the object of interest.en
dc.identifier.urihttp://hdl.handle.net/2003/27395
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-15625
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823 ; 35/2010
dc.subjectindirect regressionen
dc.subjectintegrated mean squared error criterionen
dc.subjectoptimal designen
dc.subjectradon transformen
dc.subjectspectral cut-off regularizationen
dc.subjectTikhonov regularizationen
dc.subjectuniform designen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleOptimal designs for indirect regressionen
dc.typeTextde
dc.type.publicationtypereportde
dcterms.accessRightsopen access

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